Hard thermal loop resummation of the thermodynamic potential

Starting from the Phi -derivable approximation scheme at leading-loop order, the thermodynamic potential in a hot scalar theory, as well as in QED and QCD, is expressed in terms of hard thermal loop propagators. This nonperturbative approach is consistent with the leading-order perturbative results, ultraviolet finite, and, for gauge theories, explicitly gauge invariant. For hot QCD it is argued that the resummed approximation is applicable in the large-coupling regime, down to almost twice the transition temperature.